1) Field of the Invention
The present invention relates to a structural analysis program, a structural analysis method, and a structural analysis apparatus which are provided for performing a structural analysis of physical properties, and a production process of a semiconductor integrated circuit which undergoes a structural analysis in a design stage. The present invention relates in particular to a structural analysis program, a structural analysis method, and a structural analysis apparatus which are provided for performing a structural analysis by using a finite element model, and a production process of a semiconductor integrated circuit which undergoes a structural analysis using a finite element model in a design stage.
2) Description of the Related Art
In the field of the computer graphics (CG), a space is divided into voxels. The voxels are each a very small hexahedral element constituting the space. The voxel technique is used for physical simulation such as structural analysis using the finite element method. For example, the conventional structural analysis simulation is performed through the following steps.
1. Production of a geometrical shape model by a three-dimensional CAD (Computer Aided Design).
2. Production of a finite element model (conversion of the geometrical shape model into a finite element model) by a preprocessor.
3. Numerical analysis by a solver.
4. Visualization of a result of the numerical analysis by a postprocessor.
That is, a structural analysis simulation of a three-dimensional geometrical shape model can be performed through the above steps, where a three-dimensional CAD space is divided into a plurality of voxels in the stage of the production of the finite element model, and the solver is an analysis program for numerical analysis based on the finite element method.
By use of the above structural analysis simulation, stress calculation of an object represented by a geometrical shape model can be performed on a computer. Thus, it is possible to calculate strength and durability of a designed part before production of a prototype of the part is completed.
Although the structural analysis simulation is premised on capability of production of a geometrical shape model, in some technical fields, design is carried out without production of a geometrical shape model. For example, since the design of semiconductor integrated circuits (ICs) can be basically realized by the design of the wiring pattern in each layer, the semiconductor integrated circuits can be satisfactorily designed by using the two-dimensional CAD.
However, the structural analysis simulation is currently becoming necessary even in the technical fields such as the IC design in which the three-dimensional CAD is not used. For example, in design of multilayer wiring in advanced LSIs (Large Scale Integrated circuits), strength prediction for manufacturing processes is necessary.
Nevertheless, production of a geometrical shape model by use of the three-dimensional CAD for only the structural analysis simulation imposes a heavy load on the designer. Generally, it takes long time for an engineer who usually uses only a two-dimensional CAD to master operation procedures of a three-dimensional CAD, which are not easy to understand. In addition, from the viewpoint of the efficiency in design work, it is not realistic to produce a geometrical shape model by use of a three-dimensional CAD for only the structural analysis simulation every time a wiring pattern produced by a two-dimensional CAD is changed.
Further, it is difficult to automatically produce a finite element model which is appropriate for simulation of multilayer wiring in an LSI since LSIs have fine structures, and are assembled from a number of parts made of various materials. Therefore, when an accurate result is required, the number of voxels becomes great (e.g., hundreds of thousands to hundreds of millions), and the amount of calculation also becomes great. Furthermore, since it is not easy to recognize from a three-dimensional model a complex assembly structure of multilayer wiring in an LSI, a voxel having a size which is inappropriate from a viewpoint of the structure of the LSI can be produced when the sizes and shapes of voxels are defined based on a geometrical shape model.